广义投影型的超线性收敛算法

数学物理学报 ›› 1997, Vol. 17 ›› Issue (1): 55-63.

广义投影型的超线性收敛算法

赖炎连¹, 朱建青², 郭文英¹

1 中国科学院应用数学所北京 100080;
2 郑州测绘学院郑州

收稿日期:1995-02-28 修回日期:1996-01-18 出版日期:1997-02-26 发布日期:1997-02-26
基金资助:
国家自然科学基金资助课题

A Superlinear Convergence Algorithm of Generalized Gradient Projection

Lai Yanlian¹, Zhu Jianqing², Guo Wenying¹

1 Inst. of Appl. Math. Academia Sinica, Beijing 100080;
2 Zheng Zhou Institute of Surveying and Mapping 450052

Received:1995-02-28 Revised:1996-01-18 Online:1997-02-26 Published:1997-02-26

摘要/Abstract

摘要： 该文利用矩阵分解与广义投影等技巧,给出了求解线性约束的非线性规划的一个广义投影型的超线性收敛算法,不需要δ-主动约束与每一步反复计算投影矩阵,避免了计算的数值不稳定性,利用矩阵求逆的递推公式,计算简便,由于采用了非精确搜索,算法实用可行,文中证明了算法具有收敛性及超线性的收敛速度.

关键词: 广义投影, 整体收敛性, 超线性收敛性

Abstract: In this paper,we present a superlnear convergence algorithm for nonlinear optimization with linear constraints using matrix decomposition and generalized projection techniques. The algorithm nees not to search the set of δ-active constraints and only needs one computation to the proective matrix at each itertion. Numerical instability of computation is avoided. The algorithm is practical because inexact linear search is adopted and the iterative formula of inverse matrix are given too. The convergence theorem and superlnear convergence rate theorem of the algorithm are proved.

Key words: matrix decomposition, generalized gradient projection, globol conrergence, Superlinear convergence

赖炎连, 朱建青, 郭文英. 广义投影型的超线性收敛算法[J]. 数学物理学报, 1997, 17(1): 55-63.

Lai Yanlian, Zhu Jianqing, Guo Wenying. A Superlinear Convergence Algorithm of Generalized Gradient Projection[J]. Acta mathematica scientia,Series A, 1997, 17(1): 55-63.

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